This seems to be in the same spirit as audiophiles claiming they can hear the difference between various speaker cables, or the "hints of dark chocolate" in wine tasting. Personally I see zero differences in the images on that page and unless the author has some really super-human vision abilities (possible! but unlikely) my guess is he doesn't either. WebP looks perfectly fine to me.
It's very easy to see the banding if you have a half-decent monitor. You don't even need to view the images fullscreen - and I say that as someone short-sighted with deuteranomaly.
The artefacts are visible mostly in the background, where frankly I do not care.